Varndell grabbed his treble after just 13 minutes as Wasps made easy work of Italians Mogliano at Adams Park with a thumping 71-7 victory.
Wasps eventually ran in 11 tries as Chris Bell, James Cannon, Jack Wallace, Charlie Davies (two), Tom Lindsay, Marco Wentzel and Andrea Masi all followed.
The victory saw Wasps open a six-point lead over Bayonne with only one round of pool games remaining.
Varndell crossed in the opening minute and added two more in quick succession before Dai Young's side wrapped the bonus point up three minutes later through centre Bell.
Lock Cannon and wing Wallace also crossed before half-time while Davies kicked off the second half with a double.
Mogliano registered their solitary try through Edoardo Candiago which Enrico Endrizzi converted though Wasps resumed the rout to reach the knock-out stage.
Bath squeezed past Agen 19-16 in Pool Four to secure their place in the quarter-finals.
Tom Heathcote's penalty settled a tense clash at the Recreation Ground to extend Bath's 14-game unbeaten record in this tournament
It put the gloss on a mixed afternoon for the young fly-half who missed a string of kicks before landing two decisive penalties in the second half.
Heathcote traded early penalties with opposite number Raphael Lagarde before Wales prop Paul James scored Bath's only try for a 13-9 lead at half-time.
Lagarde was shown a yellow card on the 44th minute. Heathcote extended Bath's slender lead only for Agen to tie the scores through No 8 Uelenitoni Fono before striking the winner to secure top spot in the group.
Worcester thrashed Femi-CZ Rovigo 80-17 in Pool Two thanks to 12 tries at Stadio Comune Mario Battaglini.
Josh Drauniniu grabbed a hat-trick as Worcester romped to their second 80-point away win in this campaign.
Nikki Walker, Blair Cowan and Max Stelling all crossed twice while Jake Abbott, Andy Short and Neil Best all weighed in as Worcester ran riot.
Danny Gray kicked 20 points yet that still may not be enough to progress with Perpignan sat in the driving seat in the pool after winning 50-15 at Bizkaia Gernika.
Perpignan and Worcester are level on points in Pool Two though the French side will progress if they remain tied after out-scoring the Warriors three tries to one in their two meetings.
London Welsh claimed their first home European win after beating Cavalieri Prato 62-5 in Pool Five at the Kassam Stadium.
The Exiles ran in nine tries on their way to completing the double over the Italian minnows.
Lyn Jones' side left it late to win in Italy but got off to a flying start through Lee Beech after just seven minutes.
Hooker Daniel George, Jason Lewis and Tom Arscott then followed to wrap up a bonus point before half-time.
Aled Davies, Phillip Mackenzie and Arscott then confirmed the victory before Ashley Smith and Mike Hill crossed late.
Five Clement Darbo penalties saw Grenoble defeat Stade Francais 15-9 and means the Paris club must take a point in Saturday’s home finale with London Welsh to secure a last-eight berth.